This, then, is all which seems necessary to be said respecting the occasions on which we apply Relative Terms, and to show what it is which they distinctively mark, in the trains of our sensations and ideas.
ABSTRACT RELATIVE TERMS.
From the Concrete relative terms, Abstract terms are formed, in the same manner as Abstract terms are formed from other Concrete terms. Thus from equal, we have equally; from unequal, unequally; from like, likeness; from unlike, unlikeness; from friend, friendship; and so on.
After what has been said about abstract terms in general, it will not be very difficult to mark what is peculiar in the nature of this species of them. We have seen that concrete, are connotative, terms; and that their corresponding abstracts have the same meaning with the concretes, that which is connoted being left out. White, for example, has a notation, and a connotation. It notes a quality, and it connotes something else, that which is white. The abstract whiteness marks what is noted by the concrete, but not what is connoted.
We are now to see, in what manner this applies to relative terms. I call two things like: two sensations, for example; let us say, sensations of red. I call sensation A, like sensation B; and, of course, sensation B, like sensation A. It is here more easy to observe distinctly what is connoted, than what is noted. What is connoted are the two sensations. They are clear and simple. What is noted is what we call their likeness. What is that? We have remarked, that, in having two sensations, the distinguishing them one from another is included; it is part of the compound process: And that in having two sensations—red, red, and two sensations red, green, the distinguishing the succession red, red, from the succession red, green, is included; it being part of the process, which, though in this case compound, and on that account obscure, is not the less wholly sensation. In the process of sensation, then, that part which consists in distinguishing one as one, another as another, and in distinguishing one succession from another; red, red, for example, from red, green,—is the part which is noted by the words like and unlike. The thing noted is not a distinct sensation, it is part of a process of sensation, and a part which, being never experienced separate by itself, it is very difficult to make a distinct subject of attention. Even that part of the process which consists in distinguishing, is to be distinguished into two parts. There is that part which consists in distinguishing the sensations from one another, as one, and one; and there is that part which consists in distinguishing the two, red, and red, from the two, red, and green. It is this latter part which is noted by the terms like and unlike. What is connoted is all the rest of the process. When, therefore, we make abstracts, from the terms like and unlike; that is, cut off the connotative part of their meaning, retaining the notative only; it is the part of the process which consists in distinguishing, not one and one, but two and two, which the terms distinctively mark.
We have also seen, and remarked, that having two sensations, one after another, and knowing them to be first one and then another, is a process of sensation and association. The pair of relatives, prior and posterior, or antecedent and consequent, taken together, names the whole of the process; each pair is in reality a compound name of a complex idea, that of a certain process, the process of having two ideas in succession, in which process the being sensible of the successiveness is part. By all concrete relatives, something is noted, something connoted. In the process which is marked by the relatives prior and posterior, part is noted, part connoted; and the part which is noted, is the part which it is difficult to make a separate object of attention,—the part which consists in being sensible of the successiveness, for which we have not a name. By its notation and connotation, taken together, each of the terms, prior, and posterior, is a name of something, and that something is very distinct; prior is a name of the first sensation and something else; posterior is a name of the second sensation, and something else. It is by connotation, however, that each is the name of its respective sensation. Their notative power relates to the something else, and not to the whole of that; because prior and posterior, beside connoting, each its own sensation, connote one another. The notation and connotation, therefore, are divided between them, in a manner which renders it difficult to shew what belongs to each. We have not names adapted to the purpose.
The word prior notes something, and connotes something. When we make from it the abstract term priority; what was connoted by the concrete, prior, is dropped; what was noted by it is retained. In the succession of ideas A, and B, priority is not the name of A, it is the name of that part of the compound process, which consists in knowing A, as the first of the two; posteriority is not the name of B, but of that part of the compound process, which consists in knowing B, as the last of the two.
There is a peculiarity, however, in the abstract terms formed from the relative concrete terms. These abstract terms are not, as whiteness, hardness, wholly void of connotation. They have a connotation of their own. The abstract of one relative of a pair, always connotes the abstract of the other; thus, priority always connotes posteriority, and posteriority priority.
This constitutes a distinction, worth observing, between the force of the abstracts formed from the pairs of relatives which consist of different names, as prior, posterior; cause, effect; father, son; husband, wife;—and those which consist of the same name, as equal, equal; like, like; brother, brother; friend, friend; and so on. Priority and Posteriority make together a compound name of something, of which, taken separately, each is not a name; Causingness and Causedness, the abstracts of cause and effect, make up between them the name of something, of which each by itself is not a name, and so of the rest. The case is different with such abstracts as likeness, equality, friendship, formed from pairs which consist of the same name. When we call A like, and B like; the abstract, likeness, formed from the one, connotes merely the abstract, likeness, formed from the other. Thus, as priority and posteriority make a compound name, so, likeness and likeness, make a compound name. But as likeness and likeness are merely a reduplication of the same word, likeness taken once very often signifies the same as likeness taken twice. Priority never signifies as much as priority and posteriority taken together; but likeness taken alone very often signifies as much as likeness, likeness, taken both together. Likeness has thus a sort of a double meaning. Sometimes it signifies only what is marked by the abstract of one of the pair, “like, like;” sometimes it signifies what is marked by the abstracts of both taken together. The same observation applies to the abstracts equality, inequality; sameness, difference; brotherhood, sisterhood; friendship, hostility; and so on.19
19 The exposition here given of the meaning of abstract relative names is in substance unexceptionable; but in language it remains open to the criticism I have, several times, made. Instead of saying, with the author, that the abstract name drops the connotation of the corresponding concrete, it would, in the language I prefer, be said to drop the denotation, and to be a name directly denoting what the concrete name connotes, namely, the common property or properties that it predicates: the likeness, the unlikeness, the fact of preceding, the fact of following, &c.
When the author says that abstract relative names differ from other abstract names in not being wholly void of connotation, inasmuch as they connote their correlatives, priority connoting posteriority, and posteriority priority, he deserts the specific meaning which he has sought to attach to the word connote, and falls back upon the loose and general sense in which everything implied by a term is said to be connoted by it. But in this large sense of the word (as I have more than once remarked) it is not true that non-relative abstract names have no connotation. Every abstract name—every name of the character which is given by the terminations ness, tion, and the like—carries with it a uniform implication that what it is predicated of is an attribute of something else; not a sensation or a thought in and by itself, but a sensation or thought regarded as one of, or as accompanying or following, some permanent cluster of sensations or thoughts.—Ed.
Among the abstract terms corresponding to relative concretes, those corresponding to cause and effect, are the only ones which, on account of their importance, require to be somewhat more particularly expounded.
Cause and Effect have not abstract terms formed immediately from themselves. One of the grand causes of their obscurity is, that they are not constant in their meaning, but are sometimes used as concretes, sometimes as their own abstracts.
Cause means “something causing;” effect, “something caused.” Causingness, therefore, is the proper abstract of cause; and causedness, the proper abstract of effect. Of two objects, A, and B, we call the one causing, the other caused, when they are not only prior and posterior, but parts of the same series; and, if we speak strictly, proximate parts. Of proximate parts of the same series, we call the antecedent, causing; the consequent, caused. Causingness, and causedness, therefore, mean antecedence and consequence, and something more. The ideas are more complex. Causingness and causedness, mean, not only antecedence and consequence, but also sameness of series, and proximity of parts.
As we have seen, that priority and posteriority, taken together, form a compound name of a certain complex idea, so causingness and causedness, taken together, form the compound name of a still more complex idea. Having frequent occasion to express that idea, a separate name for it was found necessary. Accordingly, we have the term Power, which means precisely what is meant by causingness and causedness taken together. Causation has the same meaning with Power, except that it connotes present time; Power connotes indefinite time.20
20 The term Causation, as the author observes, signifies causingness and causedness taken together, but I do not see on what ground he asserts that it connotes present time. To my thinking, it is as completely aoristic as Power. Power, again, seems to me to express, not causingness and causedness taken together, but causingness only. Some of the older philosophers certainly talked of passive power, but neither in the precise language of modern philosophy nor in common speech is an effect said to have the power of being produced, but only the capacity or capability. The power is always conceived as belonging to the cause only. When any co-operating power is supposed to reside in the thing said to be acted upon, it is because some active property in that thing is counted as a con-cause—as a part of the total cause.—Ed.
The connotation of Time, by abstract terms, is a circumstance almost always overlooked, but of which the observation is of the utmost importance to accuracy of thought.
When we have invented a number of marks to be taken in pairs, as like, like; equal, equal; antecedent, consequent; master, servant; husband, wife; father, son; owner, property; author, book; cause, effect; and so on; we have occasion for a name by which to speak of that class of names. We have invented such a name. We call those terms “Relative Terms.”
The word “Relative,” thus belongs to that class of names, which have been called “Names of Names.” As man, tree, stone, are names of things, of those clusters which we call objects; as red, green, hard, soft, are names of sensations; as courage, wisdom, anger, love, are names of complex ideas arbitrarily composed; so adjective is the name of one class of names, verb the name of another class of names; syllable, is the name of one part of a word, letter of another; and so, also, relative is the name of the class of words which have this peculiarity, that they are taken in pairs. Thus, father and son, are relative terms; prior and posterior, are relative terms; like and like, are relative terms; so equal, equal; unequal, unequal; brother, brother; friend, friend; and so on.
Relative itself corresponds with the names which it marks, in its being one of a pair; of that species of pairs, which are formed by a double use of the same word, as like, like. When we say of father and son, that they are relative terms, we mean that father is relative to son, and son relative to father.
As relative is the name of all concrete names, taken in pairs, such as like, like; friend, friend; causing, caused; so the abstract relation, formed from relative, is the name given to all the abstract terms formed from the concrete relatives: thus, equality, inequality, friendship, power, are abstract terms, which we call by a general name, relation. As Noun is the name of a certain class of words, so “Relation,” is the name of a certain class of words.
It is not, however, meant to be affirmed, that relative and relation, are not names which are also applied to things. In a certain vague, and indistinct way, they are very frequently so applied. This, however, is strictly speaking, an abuse of the terms, and an abuse which has been a great cause of confusion of ideas. In this way, it is said, of two brothers, that they are relative; of father and son, that they are relative; of two objects, that they are relative in position, relative in time; we speak of the relation between two men, when they are father and son, master and servant; between two objects, when they are greater, less, like, unlike, near, distant, and so on.
What, however, we really mean, when we call two objects relative (and that is a thing which it is of great importance to mark) is, that these objects have, or may have, relative names. On what accounts we give them relative names, has just been explained, and the explanation need not be repeated. When we say that Socrates and the Emperor Napoleon are unlike, the men are, each, a man, distinct, separate, absolute. We only give them a pair of related names, for the convenience of discourse. In like manner, Charles I. and George IV. are separate, distinct, absolute individuals. We only give them the relative names Predecessor, Successor, for the convenience of discourse, to mark the place which they occupied in a certain series of events. From this appears also what is meant, when we say of two objects, that they have a relation to one another. The meaning is, that the objects may have relative names, and that these names may have abstracts which we call relation. Thus we say that two brothers have a relation to one another. That relation is brotherhood. But brotherhood is merely the abstract of the relative names. We say that father and son have a relation. That relation is fathership and sonship. These are merely the abstracts of the two relative names. We say of two events, a stab with a sword, and death of the person stabbed, that they have a relation to one another. That relation is causingness and causedness, the abstract of cause and effect, or, in one word, power.21
21 The application of the word Relative to Things is not only an offence against philosophy, but against propriety of language. The correct designation for Things which are called by relative names, is not Relative, but Related. A Thing may, with perfect propriety both of thought and of language, be said to be related to another thing, or to have a relation with it—indeed to be related to all things, and to have a prodigious variety of relations with all; because every fact that takes place, either in nature or in human thought, which includes or involves a plurality of Things, is the fundamentum of a special relation of those Things with one another: not to mention the relations of likeness or unlikeness, of priority or posteriority, which exist between each Thing and all other Things whatever. It is in this sense that it is said, with truth, that Relations exhaust all phenomena, and that all we know, or can know, of anything, is some of its relations to other things or to us.—Ed.
SECTION III.
NUMBERS.
We have already observed, that objects exist, with respect to us, in two orders; in the synchronous order, and the successive order; and that we have great occasion for marks to represent them to us as they exist in both orders. We have also to observe, that the synchronous order, the order in which things exist together; that is, as we otherwise name it, the order of position, or the order in place; is interesting to us chiefly on account of the successive order. The order in which objects succeed one another, that is, the order of the changes which take place, the order of events, depends almost entirely upon the synchronous order. In other words, the synchronous order is part of every successive order; it is the antecedent of every consequent; or as we otherwise express it, the cause of every effect. Thus the synchronous order, or the order in place, of the spark and the gunpowder, is the antecedent of the explosion; the synchronous order of my finger and the candle, is the antecedent or the cause of the pain which I feel.
In regard to the explosion, also, it is less or greater, according as the quantity of the gunpowder is less or greater. Of the synchronous order, therefore, one part which I am particularly interested in knowing correctly is, the amount of the things. A certain amount of gunpowder produces one set of effects, another another: a certain amount of men produce one set of effects, another another; and so of all other things.
It is of the last importance to me not only to be able to ascertain, and know, these amounts, with accuracy, but to be able to mark them.
For ascertaining and knowing amounts, some contrivance is requisite. It is necessary to conceive some small amount, by the addition or subtraction of which, another becomes larger or smaller. This forms the instrument of ascertainment. Where one thing, taken separately, is of sufficient importance to form this instrument, it is taken. Thus, for ascertaining and knowing different amounts of men, one individual is of sufficient importance. Amounts of men are considered as increased or diminished by the addition or subtraction of individuals. A grain of gunpowder might also be taken; but it is not of sufficient importance; the quantity, taken as the instrument of measurement, must have an ascertainable influence upon the effect, for the sake of which, the ascertaining of the amount is of importance. In their simple state, men use principally the hand for their elementary ascertainments. A pinch, or as much as could be held between the finger and the thumb, was a small amount distinctly conceived, and formed the principle of measurement where small additions were important; a handful was not less distinctively conceived, and was the instrument, where only larger additions were of importance.
When one addition was made, or needed to be made, after another, and another after that, and so on, the next point of importance was to conceive exactly how often the addition was made. A few additions are distinct to sense. Place one billiard-ball by another, the sight of the two is distinct. Place three or four, it is still distinct. Soon, however, it ceases to be so. Place a dozen, and you will not probably be able to distinguish them from eleven. You must count them, or divide them. If you divide them by the eye, into two parcels, you may see that one is six and another six; but to benefit by this, you must know the art of putting six and six together.
The next step, therefore, necessary in the process of ascertaining amounts, was, to mark these additions, one after another, in such a manner, as to make known to what extent they had gone. When men were familiar with the operation of assigning names as marks of their ideas, the course which would suggest itself to them is obvious; they would employ a name as the mark of each addition. They would say, one, for the first, two, for the second, three, for the third, and so on. These marks it was very useful to make connotative, that the other important ingredient of the process, the thing added, might be made known at the same time. Thus we say, one man, two men; one horse, two horses; and so of all other things, the enumeration of which we are performing.
Numbers, therefore, are not names of objects. They are names of a certain process; the process of addition; of putting one billiard-ball to another; not more mysterious than any other process, as walking, writing, reading, to which names are assigned. One, is the name of this once performed, or of the aggregation begun; two, the name of it once more performed; three, of it once more performed; and so on. The words, however, in these concrete forms, beside their power in noting this process, connote something else, namely, the things, whatever they are, the enumeration of which is required.
In the case of these connotative, as of other connotative marks, it was of great use to have the means of dropping the connotation; and in this case, it would have been conducive to clearness of ideas, if the non-connotative terms had received a mark to distinguish them from the connotative. This advantage, however, the framers of numbers were not sufficiently philosophical to provide. The same names are used both as connotative, and non-connotative; that is, both as abstract, and concrete; and it is far from being obvious, on all occasions, in which of the two senses they are used. They are used in the connotative sense, when joined as adjectives with a substantive; as when we say two men, three women; but it is not so obvious that they are used in the abstract sense, when we say three and two make five; or when we say fifty is a great number, five is a small number. Yet it must, upon consideration, appear, that in these cases they are abstract terms merely; in place of which, the words oneness, twoness, threeness, might be substituted. Thus we might say, twoness and threeness are fiveness.22 23
22 The vague manner in which the author uses the phrase “to be a name of” (a vagueness common to almost all thinkers who have not precise terms expressing the two modes of signification which I call denotation and connotation, and employed for nothing else) has led him, in the present case, into a serious misuse of terms. Numbers are, in the strictest propriety, names of objects. Two is surely a name of the things which are two, the two balls, the two fingers, &c. The process of adding one to one which forms two is connoted, not denoted, by the name two. Numerals, in short, are concrete, not abstract names: they denote the actual collections of things, and connote the mental process of counting them. It is not twoness and threeness that are fiveness: the twoness of my two hands and the threeness of the feet of the table cannot be added together to form another abstraction. It is two balls added to three balls that make, in the concrete, five balls. Numerals are a class of concrete general names predicable of all things whatever, but connoting, in each case, the quantitative relation of the thing to some fixed standard, as previously explained by the author.—Ed.
23 Here the process of numeration generally, together with the function of numbers carrying their separate names, are clearly set forth; after which we find the remark, that no distinction is made in the name of the number, when used as an abstract and when used as a concrete. Mr. James Mill thinks that it would have been conducive to clearness if such distinction had been marked by an inflexion of the name. “The names of numbers are used in the connotative (concrete) sense, when joined as adjectives with a substantive, as when we say, two men, three men: but it is not so obvious that they are used in the abstract sense, when we say three and two make five: or when we say fifty is a great number, five is a small number. Yet it must upon consideration appear, that in these cases they are abstract terms merely: in place of which, the words oneness, twoness, threeness, might be substituted. Thus we might say, twoness and threeness are fiveness.”
The last part of what is here affirmed cannot, in my judgment, be sustained. Connecting itself with one among the many arguments between Aristotle and Plato, it lays down a position from which both of them would have dissented. In the last book but one (Book M) of Aristotle’s “Metaphysica,” this argument will be found set forth at length; though with much obscurity, which is cleared up by the lucid commentary of Bonitz. Plato distinguished two classes of numbers—the mathematical, and the ideal. The first class were the Quanta of equal and homogeneous units (One, Two, Three, &c.), any or all of which might be added so as to coalesce into one total sum. The second class were, the ideal or abstract numbers, Two quatenus Two, &c., represented by Dyad, Triad, Tetrad, Pentad, Dekad, &c., the characteristic property of which was, that they could not be added together nor coalesce into one sum. These were uncombinable numbers, “ἀριθμοὶ ἀσύμβλητοι—numeri inconsociabiles.”—See Aristot. Metaph. M. 6. 1080. b. 12. Bonitz Comment. p. 540, 541, seq.
Plato regarded these uncombinable numbers as the highest representative specimens or coryphæi of the Platonic Ideas. In this character Aristotle reasoned against them, contending that they did nothing to remove the many objections against Plato’s ideal theory. With the question thus opened, I have no present concern: all that I wish to point out is the view which Plato originated and upon which Aristotle reasoned, viz.: That these ideal or abstract numbers could not be added together, or fused into one sum total. The abstract term Twoness means Two so far forth as two: so also Threeness and Fiveness. You cannot truly predicate anything of Twoness which would be inconsistent with this fundamental characteristic: you cannot add it to Threeness so as to make Fiveness, nor can you subdivide Fiveness into Twoness and Threeness, without suppressing the fundamental characteristic of each. Neither of them admit of increase or diminution. In like manner, a Triangle, or every particular Triangle, may have one of its sides taken away, or two more sides added to it: on each of which suppositions it ceases to be a triangle. But if we speak of a Triangle so far forth as Triangle, neither of these suppositions is admissible. We may say that its three angles are equal to two right angles, but we cannot subtract from it one of its sides, nor add to it one or two other sides. The subject of predication is so limited and specialised, that no predicate can be allowed which would efface its characteristic feature—Triangularity.
Bonitz remarks truly that the class of numbers set forth by Plato—the ideal or uncombinable numbers which could not be either added or subtracted—were divested of all the useful aptitudes and functions of numbers, and passed out of the category of Quantity into that of Quality. The Triad was one quality; the Pentad was another: there was no common measure into which both could be resolved (Bonitz, Comment. p. 540—553). Two, three, five, are quantifying names, designating each so many numerable units: and the units counted in each list may be added to, or subtracted from, the units counted in the others. But when we say, Twoness or the Dyad—Threeness or the Triad—Fiveness or the Pentad—we then recognise a peculiar quality, founded upon each separate variety of aggregation or quantification: so that these separate varieties are no longer resolvable into any common measure of constituent units. Each quality stands apart from the others, and has its own predicates. In the view of Plato and the Pythagoreans, the Dekad especially was invested with magnificent predicates.
I cannot therefore agree with Mr. James Mill in his opinion that, “when we say three and two make five, we use these numbers in the abstract sense.” We clearly do not mean that three, so far forth as three, and two, so far forth as two, make five. But this would be what we should mean, if we used these names of numbers in the abstract sense. What we do mean is, that the units constituting three may be added to those constituting two, so as to make five: and that this is equally true, whether the units are men, horses, stones, or any other objects. Two, three, five, &c., are general or universal terms, capable of being joined with units of indefinite variety: but they do not become abstract terms, until we limit them by quâtenus, καθόσον, ᾗ, so far forth as, &c., or by a suffix such as ness. Such abstracts would have been of little use as to the ordinary functions of numbers; and accordingly they have never got footing in familiar speech, though they are occasionally employed in metaphysical discussions.—G.
It is necessary to observe, that the process, marked by the names called numbers, though used for the purpose of ascertaining synchronous order, is in the mind successive; one addition follows another. Numbers, therefore, in reality, name successions; and are easily applied to mark certain particulars of the successive order, when the marking of those particulars is of importance.
It is of importance, when successions take place all of one kind; and when consequences of importance depend upon the less or greater length of the train. It is then of importance, to mark the degrees of that length, which is correctly done by the enumeration of the links.
To take a simple and familiar instance, that of the human steps. They are successions all of one kind. Consequences of importance may, and often do result from a knowledge of the length of any particular series of steps. The ascertainment of an aggregate, in this order, is made in the same way, as that which we have traced in the synchronous order. An element of aggregation is taken; by its successive aggregations, the amount of the aggregate is correctly conceived; and, by a proper mark for each successive aggregation, it is also correctly denoted. The continued successions of day and night are all of one kind; and it is of the greatest importance for us to know accurately the length of a series of those successions; of the series between such and such events; between the sowing of the seed in the ground, for example, and the maturity of the crop. This is done, accurately, by putting a several mark upon each several succession, one for the first, two for the one after that, three for the one after that, and so on.
If there be no mystery in one sensation after another, or one idea after another; and, if having them in that order and associating the idea of the antecedent with the sensation of the consequent be to know that they are in that order; then there is no mystery in Numbers, for they are only marks to shew that one is after another.
That there is no mystery in the ideas of priority and posteriority, which are relative terms, has been shewn under the preceding head of discourse.
The word Number itself, which is only a name of the names, one, two, &c., nothing being a number but some one of those names, has also been explained, when the class of words which are distinguished as Names of Names was under consideration.
In using the terms, one, two, three, four, and so on, the object is to ascertain with precision, the amount of the aggregate in question. In some cases, however, it is of importance to ascertain the order of aggregation, as well as the amount; and that, whether a synchronous, or a successive, aggregate be the object in view. This purpose is answered by a set of names, called the ordinal numbers, which, applied to the units of aggregation in the order in which they are taken, mark precisely the order of each. Thus, when we say, first, second, third, fourth, and so on; each of these concrete, or connotative names, notes a certain position, if in the synchronous order; a certain link, if in the successive; and connotes the precise object which holds that position, or forms that link.
As there is no difficulty whatsoever in tracing the ideas, which, on each occasion, receive those marks, there is no need of multiplying words in their illustration.
SECTION IV.
PRIVATIVE TERMS.
Privative terms are distinguished from other terms, by this; that other terms are marks for objects, as present or existent; privative terms are marks for objects, as not present or not existent.24
24 The author gives the name of Privative terms to all those which are more commonly known by the designation of Negative; to all which signify non-existence or absence. It is usual to reserve the term Privative for names which signify not simple absence, but the absence of something usually present, or of which the presence might have been expected. Thus blind is classed as a privative term, when applied to human beings. When applied to stocks and stones, which are not expected to see, it is an admitted metaphor.
This, however, being understood, there is no difficulty in following the author’s exposition by means of his own language.—Ed.
Thus the word Light, is the mark of a certain well-known object, as existent or present.
The word Darkness, on the contrary, is the mark of the same object, as not existent or not present. Ask any man, what he means by darkness; he says the absence of light. But the absence of light, is only another name for light absent; and light absent, is only another name for light not present. Darkness, therefore, is another name for light not present.
It thus appears, that the idea called up by the word light, is that of a certain object associated with its presence; the idea called up by the word darkness, is that of the same object associated with its absence.
After the explanations which have been so often given, what I mean, when I speak of the idea of an object, as one thing; the idea of its presence, as another thing; ought not to be obscure. Its presence, is its existence; its absence, is its non-existence; at least, at a particular time and place. What ideas and sensations I mark by the word existent, has already been explained. The word non-existent is the mere negation of the same sensations and ideas.
We have repeatedly seen, that what we call existence, is an inference from our sensations. We have clusters of sensations; these call up the ideas of antecedents, which we call qualities; these the idea of an antecedent common to all the qualities, which we call Substratum; and the Substratum, with its qualities, we call the Object.
When we speak, then, of this Substratum and its qualities, as present, at a particular time and place: which is what we mean by its existence; what we affirm is this; that if there be sentient organs at such a time and place, there will be such and such sensations. When we speak of it as absent, we affirm, that though there be sentient organs at such a time and place, there will not be those sensations. These ideas, then, forming in combination a very complex idea, are what, in the respective cases, we call the presence, and the absence of an object. Any further analysis would be superfluous in this place.
A law of some importance, which has been already explained, is, that in complex ideas there is very often some one part, so prominent, as to throw the rest into the shade, and confine the attention almost wholly to itself. There is a curious exemplification of this law, in the pair of cases before us. Thus, in the complex idea of “the object and its presence,” marked by the word Light, the object is the prominent part, and the presence is so habitually neglected, that it is with some trouble it is recognised. The case is reversed in the complex idea of “the object and its absence,” marked by the word Darkness. In this, the absence is the prominent part, and it so completely engrosses the attention, that it requires reflection, to discover, that the idea of the object is necessarily combined.
There is something more in these two cases, which it is of great importance to remember. We have two sets of indissoluble associations, both exceedingly numerous, the one with the idea of the object as present, the other with the idea of it as absent; that is, the one set with light, the other set with darkness. Whenever we have the perception of light, we habitually have, along with it, the perception of objects; that is, of all sorts of colours, all sorts of shapes, all sorts of magnitudes, all sorts of distances, and so on. With the idea of light, then, are indissolubly associated the ideas of all sorts of objects; of extension in all its modifications, colour in all its modifications, motion in all its modifications; the word light, therefore, serves as a name, not merely of the fluid which acts upon the eye, but of that along with its innumerable associations. Such are the perceptions and ideas, which, when we have the perception of light, we have along with it. What are the perceptions and ideas, which, when we have not the perception of light, we have along with that state of privation? There is, first, the want of all the perceptions, which we have along with that of light. There is, next, the disagreeable sensations we experience from not knowing what objects are approaching us, either by our motions, or by theirs; hence the idea of dangerous objects approaching; hence, also, the inability to perform many of the acts which are conducive either to our being, or well-being. With the idea of darkness, then, are indissolubly associated a multitude of ideas, of pain, of privation, of weakness; all disagreeable; with little or no mixture of any of an opposite kind. And the word darkness, therefore, stands as a name not merely of light absent, but of that along with all the accompanying sensations and ideas.
The reader will observe, and it is necessary he should well observe, that all terms might have corresponding privative terms. We have already stated, that the ordinary names of objects are names both of the object, and of its presence or existence, combined in one complex idea. Thus, rose, horse, are names of the objects as present or existent. We might have had names of them as absent or not existent. It is only, however, in a few cases, that the absence of an object is a matter of first-rate importance. It is only in those cases that it has been found requisite to have for it a particular name. The absence of light is obviously a case of the greatest importance. Consequences of the very first order, and infinite in number, depend upon it. An appropriate name, therefore, was of the highest utility.
This explanation will enable us to see, without a minute analysis, the composition of the clusters marked by other Privative Terms.
Let us take Silence, as the next example. Silence is the absence of sound, either all sound, which is sometimes its meaning; or of some particular sound, which at other times is its meaning. Sound is the name of a well-known something, as present. Silence is the name of the same well-known something, as absent. The first word, is the name of the thing, and its presence. The second, is the name of the thing, and its absence. In the case of the combination marked by the first, namely, the thing and its presence, the thing is the prominent part, and the presence generally escapes attention. In the case of the second, the thing and its absence, the absence is the important part, and the thing is feebly, if at all, attended to.
Ignorance is easily explained, in the same manner. Knowledge is the name of a certain well-known something, as present or existent. Ignorance is the name of the same well-known something, as absent or nonexistent.
Having a sensation, or an idea, is one state of consciousness; not having it is another state of consciousness.2* The state of consciousness called “not having” it is no doubt very various; for it is any sensation or idea different from the one in question. The “Having” one sensation and another sensation, or one idea and another idea; and the “Knowing” that the one is not the other; we have often observed to be the same thing. The great majority of names are invented, to mark sensations and ideas as “had;” there are, however, cases, in which it is necessary to mark them as “not had.” In what manner, in the more remarkable cases, this marking is performed by privative names, has now been shewn. But, beside the marks for particular cases, it was necessary to have a comprehensive or general mark; which should include all cases, as well those provided with particular names, as those not so provided. “Absent” was such a word. “Absent,” standing by itself, and unrestricted by connection with any other word, is a name of any thing, joined with the idea of its not being then and there. What is included in that Idea has already been shewn in explaining Belief in Existence. The mark “Absent,” joined with any particular name, becomes a particular Privative Term. We have observed, that the word rose, is a mark not merely of the thing, but the thing with the idea of its presence; we have also observed, that such Presence-affirming Terms, except in remarkable cases, have not corresponding Privative, or Absence-affirming Terms. But if we say “absent” rose, we have a Privative Term, double worded, indeed, instead of single worded, exactly corresponding to the Presence-affirming Term, rose. And, by the use of the same word, we can form Privative Terms of this description, in all cases in which they can be wanted; thus we can say, absent man, absent horse, absence of food, &c.
2* Mr. Locke recognised the fact, but gave an erroneous account of it: “I should offer this as a reason why a privative cause might produce a positive idea; viz., that, all sensation being produced in us, only by different degrees and modes of motion in our animal spirits, variously agitated by external objects, the abatement of any former motion, must as necessarily produce a new sensation, [for “abatement of any former motion,” read, ceasing of a particular sensation; and for “new sensation,” read, new feeling, or, new state of consciousness,] as the variation or increase of it: and so introduce a new idea. B. II. ch. viii. s. 4.—(Author’s Note.)
The word Nothing, Nihil, is another generical Privative Term. That this word has a very important marking power, every man is sensible in the use which he makes of it. But if it marks, it names; that is, names something. Yet it seems to remove every thing; that is, not to leave anything to be named.
The preceding explanations, however, have already cleared up this mystery. The word Nothing is the Privative Term which corresponds to Every Thing. Every Thing is a name of all possible objects, including their existence. Nothing is a name of all possible objects, including their non-existence.25
25 The analysis of the facts, in all these cases, is admirable, but I still demur to the language. I object to saying, for instance, that silence is “the name of sound and its absence.” It is not the name of sound, since we cannot say Sound is silence. It is the name of our state of sensation when there is no sound. The author is quite right in saying that this state of sensation recalls the idea of sound; to be conscious of silence as silence, implies that we are thinking of sound, and have the idea of it without the belief in its presence. In another of its uses, Silence is the abstract of Silent; which is a name of all things that make no sound, and of everything so long as it makes no sound; and which connotes the attribute of not sounding. So of all the other terms mentioned. “Nothing” is not a name of all possible objects, including their non-existence. If Nothing were a name of objects, we should be able to predicate of those objects that they are Nothing. Nothing is a name of the state of our consciousness when we are not aware of any object, or of any sensation.—Ed.
“Absent,” in its unrestricted sense, above explained, comes near to this marking power of the word Nothing, but differs from it in one respect. Absent is the Privative name of all possible objects, taken one by one. Nothing is the privative name of them, taken altogether. This distinction, I presume, is sufficiently obvious, and intelligible, thus expressed; and stands in no need of a more wordy explanation.3*
3* The account of Privative Terms which is given by Locke, is the same with that which is presented in the text. The difference is, that Locke, who has stated the case correctly, has not attempted its analysis. He says (B. II. ch. viii.), “We have negative names, such as insipid, silence, nihil, &c., which words denote positive ideas; v.g., taste, sound, being; with a signification of their absence.”—(Author’s Note.)
We shall now take notice of the Privative Term EMPTY, which is a word of great importance.
Empty is a name applicable to all the things to which the name, full, is applicable; in other words, to all the things which are calculated to contain other things in position, or in the synchronous order, that is, in the order of particle adjoining particle. It is necessary to mark this limitation of the word contain; because, in another sense, a complex idea is said to contain the simple ideas of which it consists; and a chemical compound is said to contain the simple substances into which it can be decomposed. Empty, and Full, are names of those things only which contain, or are adapted to contain, things in position, or in the order of particle adjoining particle.
Things adapted to contain other things in position, are, themselves, a peculiar combination of positions, to which we must very attentively advert. To understand this combination, it will be necessary to remember exactly the analysis of position; of lines, surfaces, and bulks; as it has been already given in our explanation of Relative Terms.
The word “containing,” applied to anything, as when we speak of a box containing books, a cask containing liquor, a room containing furniture, generally includes the idea of limitation. That which contains, has certain boundaries within which the things contained are placed, or have their position. This idea of things having their position within another thing, is a very complex idea, the composition of which we must be at some pains to understand.
It consists, first, of the thing containing; secondly, of the things contained.
The thing containing, again, consists of two parts; first, its boundaries; and, secondly, its containing capacity within its boundaries.
Its boundaries are surfaces. How we become acquainted with surfaces; in other words, what are the sensations, the copies of which form our complex idea of surface, has been already explained. They are certain sensations of touch, and certain sensations of muscular action. This complex idea is easily distinguished into two parts; first, a certain idea of resistance; secondly, the idea of extension. The sides of a box I call resisting, and I call them extended; and I call them by both names on account of certain sensations. Let us conceive the box without a lid; each of the sides is extended and resisting. What is the top without a lid? Extended, and non-resisting. The idea of the top is that of extension without resistance; extension, in a particular direction, that of a plane surface. What is the idea of the inside of the box without its contents? That of extension in all directions without resistance. This is emptiness.
So far is plain, and not doubtful. There are still, however, some things which require explanation. What are we distinctly to understand by extension without resistance? Whenever we use the concrete extended, we mean something extended; and by that something we always mean something that resists. What do we mean when we use the abstract extension? It will be easily recollected that all this is a case of association, which has been already fully explained.
Concrete Terms are Connotative Terms; Abstract Terms are Non-connotative Terms. Concrete terms, along with a certain quality or qualities, which is their principal meaning, or notation, connote the object to which the quality belongs. Thus the concrete red, always means, that is, connotes, something red, as a rose. We have already, by sufficient examples, seen, that the Abstract, formed from the Concrete, notes precisely that which is noted by the Concrete, leaving out the connotation. Thus, take away the connotation from red, and you have redness; from hot, take away the connotation, and you have heat.
The very same is the distinction between the concrete extended, and the abstract extension. What extended is with its connotation, extension is without that connotation. We have then to explain, wherein the connotation consists.
When we say extended, meaning something extended, we mean one or other of three things, a line, a surface, or bulk. We have already explained sufficiently in what manner we come by the ideas of line, surface, and bulk. We have certain sensations of touch, and of muscular action, conjoined, and the ideas of those sensations, in conjunction, form our ideas of line, surface, and bulk. The sensation, or sensations, which we mark by the word resisting, seem to be those alone which are connoted by the word extending; for it is most important to observe, that what we call extending in the parts of our own body, by the operation of its own muscles, is that which we call extended in all other things; and thus the essential connotation of the concrete, extended, is, resisting, and nothing else. In other concrete terms the connotation is greater. Thus red, connotes a surface, that is, something extended; and extended connotes resisting. And thus red connotes both extended and resisting, while extended connotes resisting alone. It is true, that persons enjoying the faculty of seeing cannot conceive any thing extended, without conceiving it coloured; because in them the idea of something extended includes, by association, the visual, as well as the tactual, and muscular, ideas; and the visual being accustomed to predominate, the tactual, and muscular, are faintly observed. This, however, cannot be the case in persons born blind, who have the tactual, and muscular, feelings, and not the visual at all.
Now, then, we can easily understand what extension is in all its cases. Linear extension is the idea of a line, the connotation dropped, that is, the idea of resisting, dropped; superficial extension is the idea of a surface, the same connotation dropped; and solid extension, or bulk, is merely the idea of bulk, the connotation, or resisting, dropped. But bulk, the connotation (i.e. resistance) dropped, is what? The place for bulk: Position. But place is, what? A portion of SPACE; or, more correctly speaking. SPACE itself, with limitation.
We thus seem to have arrived, without any difficulty, at an exact knowledge of what is noted or marked by the word SPACE; a phenomenon of the human mind hitherto regarded as singularly mysterious. The difficulty which has been found in explaining the term, even, by those philosophers who have approached the nearest to its meaning, seems to have arisen, from their not perceiving the mode of signification of Abstract Terms; and from the obscurity of that class of sensations, a portion of which we employ the word “extended” to mark. The word “space” is an abstract, differing from its concrete, like other abstracts, by dropping the connotation. Much of the mystery, in which the idea has seemed to be involved, is owing to this single circumstance, that the abstract term, space, has not had an appropriate concrete. We have observed, that, in all cases, abstract terms can be explained only through their concretes; because they note or name a part of what the concrete names, leaving out the rest. If we were to make a concrete term, corresponding to the abstract term space, it must be a word equivalent to the terms “infinitely extended.” From the ideas included under the name “infinitely extended,” leave out resisting, and you have all that is marked by the abstract Space.26
26 There is great originality as well as perspicacity in the explanation here given of Space, as a privative term, expressing when analysed, the absence of the feeling of resistance in the circumstances in which resistance is frequently felt, namely, after the sensations of muscular action and motion. The only part of the exposition to which I demur is the classing of Space among abstract terms. I have already objected to calling the word line, when used in the geometrical sense, an abstract term. I hold it to be the concrete name of an ideal object possessing length but not breadth. In like manner a Space may be said to be the concrete name of an ideal object, extended but not resisting. The sensations connoted by this concrete name, are those which accompany the motion of our limbs or of our body in all directions: and along with these sensations is connoted the absence of certain others, viz. of the muscular sensations which accompany the arrest of that motion by a resisting substance. This being the meaning of a Space, Space in general must be a name equally concrete. It denotes the aggregate of all Space.—Ed.
In the idea of SPACE, the idea of Infinity is included. What the idea of Infinity is, needs therefore to be explained. When the word Infinite is not used metaphorically, as it is when we speak of the infinite perfections of God, in which case it is not a name for ideas, but for the want of them, it is applied only to Number, Extension, and Duration.
We increase numbers by adding one to one, one to two, and so on, without limit, giving a name to each aggregate. The association of ideas which constitutes the process has been already explained. With each number, one, two, three, four, as we go on, the idea of one more is so strongly associated, that we cannot help its existing in immediate conjunction. However high, therefore, we go in numbering, the idea of one more always forces itself upon us; and hence we say that number is infinite. That this, literally, is not true; that, indeed, it is a verbal contradiction, is obvious. Number, is something numbered; but if numbered, limited; that is, not infinite. Number is the negation of infinite; as black is the negation of white. The name infinite, in this case, is, in reality, nothing but a mark for that state of consciousness, in which the idea of one more is closely associated with every succeeding number. And Infinity, the abstract term, is the peculiar idea, without the connotation.
When we apply “infinite” to extension, we do so equally to all its three modifications, to lines, surfaces, and bulk. How we do so is obvious. We know no infinite line, but we know a longer, and a longer. A line is lengthened, as number is increased, by continual additions; a line of any length, say of an inch, is increased by the continual addition of other lengths, say of an inch. In the process, then, by which we conceive the increase of a line, the idea of one portion more, is continually associated with the preceding length; and to what extent soever it is carried, the association of one portion more, is equally close and irresistible. This is what we call the idea of infinite extension; and what some people call the necessary idea; which only means, that the idea of a portion more, rises necessarily, that is, by indissoluble association, so that we cannot help its rising. Infinite is the concrete term, here connoting Line; drop the connotation, you have Infinity, the abstract.
If such be the whole of what is involved in the idea of Infinity, in the case of a line; call it necessary idea, if you will; the idea of it, in the case of surface, and of bulk, is also explained; for surface, and bulk, are only lines, in such and such, or in all directions. The idea of a portion more, adhering, by indissoluble association, to the idea of every increase, in any or in all directions, is the idea of “infinitely extended,” and the idea of “infinitely extended,” the connotation dropped, is the idea of Infinite Space. It has been called a simple idea (so little has the real nature of it been understood); while it is thus distinctly seen, to be one of the most complex ideas, which the whole train of our conscious being presents. Extreme complexity, with great closeness of association, has this effect—that every particular part in the composition is overpowered by the multitude of all the other parts, and no one in particular stands marked from the rest; but all, together, assume the appearance of ONE. Something perfectly analogous occurs, even in sensation. If two or three ingredients are mixed, as wine and honey, we can distinguish the taste of each, and say it is compound. But if a great many are mixed, we can distinguish no one in particular, and the taste of the whole appears a simple peculiar taste.27
27 This explanation of the feeling of Infinity which attaches itself to Space, is one of the most important thoughts in the whole treatise; and, obvious as its truth is to a mind prepared by the previous exposition, it has great difficulty in finding entrance into other minds.
Every object is associated with some position: not always with the same position, but we have never perceived any object, and therefore never think of one, but in some position or other, relative to some other objects. As, from every position. Space extends in every direction (i.e. the unimpeded arm or body can move in any direction), and since we never were in any place which did not admit of motion in every direction from it, when such motion was not arrested by a resistance; every idea of position is irresistibly associated with extension, beyond the position: and we can conceive no end to extension, because the place which we try to conceive as its end, raises irresistibly the idea of other places beyond it. This is one of the many so-called Necessities of Thought which are necessities only in consequence of the inseparableness of an association: but which, from unwillingness to admit this explanation, men mistake for original laws of the human mind, and even regard them as the effect and proof of a corresponding necessary connexion between facts existing in Nature.—Ed.
This, indeed, is one great cause of the mistakes, which have been committed, in the examination of abstract ideas. We have shewn that they are all complex, and in the highest degree. Yet the greater number of them have always been treated as simple. Mr. Locke shewed that some of them, which he calls mixed modes, were undoubtedly compounded, as obligation, crime, &c. But they are no otherwise complex, than as power, quality, chance, fate, position, and space, are complex.
It is truly remarkable, how many of the cases of indissoluble association are all united in the idea of SPACE. First of all, with the idea of every object, the idea of position or place, is indissolubly united. Secondly, with the idea of position or place, the idea of extension is indissolubly united. Thirdly, with the idea of extension the idea of infinity is indissolubly united. Fourthly, by the unfortunate ambiguity of the Copula, the idea of existence is indissolubly united with SPACE, as with other abstract terms. What these several ingredients, the ideas of Position, Extension, Infinity, Existence, are composed of, we have already seen. All these, forced into combination, by irresistible association, constitute the idea of SPACE.